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arXiv · 1012.3081

The Universal RG Machine

Dario Benedetti·Kai Groh·Pedro F. Machado·Frank Saueressig
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Abstract

Functional Renormalization Group Equations constitute a powerful tool to encode the perturbative and non-perturbative properties of a physical system. We present an algorithm to systematically compute the expansion of such flow equations in a given background quantity specified by the approximation scheme. The method is based on off-diagonal heat-kernel techniques and can be implemented on a computer algebra system, opening access to complex computations in, e.g., Gravity or Yang-Mills theory. In a first illustrative example, we re-derive the gravitational $\beta$-functions of the Einstein-Hilbert truncation, demonstrating their background-independence. As an additional result, the heat-kernel coefficients for transverse vectors and transverse-traceless symmetric matrices are computed to second order in the curvature.

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Dario Benedetti, Kai Groh, Pedro F. Machado, Frank Saueressig. 2010-12-14. The Universal RG Machine. https://doi.org/10.1007/jhep06(2011)079

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